Yes, the trains do have accommodations for luggage and rather nice. You will see wonderful countryside. However, it may be just as quick to take a Ryanair flight from Dublin to Cork. If you are traveling from USA to Ire on Aer Lingus check their website for Hertz rental car; which you can actally get cheaper deal thru the Aer Lingus website then by going thru the International Hertz web site.
If you do decide to take train to Cork. You should take cab to Cork Aerport to pick up your rental. It will be easier than trying to schlep your bags to another location in town. (trust me on this one) :)
I would book the car thru to Dublin; as it will be quicker to get back to dubs via car and return car rental at Dublin Aerport, however, if you can get your ticket changed and fly out of Shannon would even be better; as it is a wonderful aerport to fly out of and you can spend more time in the West! The road from Galway to Shannon is about 45 min.